Carter, the one-term president to whom conservatives sometimes gleefully compare Obama, told CNN that Jon Huntsman, the former Republican governor of Utah who resigned last Saturday as Obama's top diplomat in China, might make for Obama's best GOP challenger.

Carter said that Huntsman is "very attractive to me personally," but also said that his "intention is to vote for the Democratic candidate."

This will be Huntsman's challenge if he runs for president: being portrayed as the left-most candidate in an increasingly right-leaning Republican Party.